Click the Contacts button in the left hand menu:
Click on the contact you wish to delete (you will see the information change to show the details and Activities for that contact), then click the delete button in the top menu:
You will then be prompted to make sure you wish to delete this contact:
Clicking Delete will remove the contact and all activities completed for this contact*. Clicking Cancel will take you back to the contacts screen.
* Please note that deleted contacts can not be recovered. Once the contact has been deleted, so will all of that contact's research.